=(3x^2-6x-12)+x^2+x+3

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Solution for =(3x^2-6x-12)+x^2+x+3 equation: 


Simplifying
0 = (3x2 + -6x + -12) + x2 + x + 3

Reorder the terms:
0 = (-12 + -6x + 3x2) + x2 + x + 3

Remove parenthesis around (-12 + -6x + 3x2)
0 = -12 + -6x + 3x2 + x2 + x + 3

Reorder the terms:
0 = -12 + 3 + -6x + x + 3x2 + x2

Combine like terms: -12 + 3 = -9
0 = -9 + -6x + x + 3x2 + x2

Combine like terms: -6x + x = -5x
0 = -9 + -5x + 3x2 + x2

Combine like terms: 3x2 + x2 = 4x2
0 = -9 + -5x + 4x2

Solving
0 = -9 + -5x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 9 = 9
9 + 5x + -4x2 = -9 + -5x + 4x2 + 9 + 5x + -4x2

Reorder the terms:
9 + 5x + -4x2 = -9 + 9 + -5x + 5x + 4x2 + -4x2

Combine like terms: -9 + 9 = 0
9 + 5x + -4x2 = 0 + -5x + 5x + 4x2 + -4x2
9 + 5x + -4x2 = -5x + 5x + 4x2 + -4x2

Combine like terms: -5x + 5x = 0
9 + 5x + -4x2 = 0 + 4x2 + -4x2
9 + 5x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
9 + 5x + -4x2 = 0

Factor a trinomial.
(9 + -4x)(1 + x) = 0


Subproblem 1
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {2.25, -1}

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